Approximation of non-monotone multivalued differential inclusions

An approximation of non-monotone, multivalued differential inclusions,the so-called hemivariationa] inequalities, is presented. Arelation between the approximation problem and the problem offinding a substationary point of an approximation of the correspondingpotential function is also established. This relation makesit possible to solve the approximated problem by using nonsmooth,non-convex optimization methods. Some numerical experimentsare also presented.     

OPTIMAL HARVESTING OF FOREST AGE CLASSES UNDER PRICE UNCERTAINTY AND RISK AVERSION

ABSTRACT. . We analyze optimal forest harvesting under mean reverting and random walk timber price and include multiple age classes, forest owners' consumption‐savings decisions and risk aversion. This framework generalizes existing studies that assume a single stand and risk neutrality or include ad hoc risk aversion and obtain the result that uncertainty lengthens the optimal rotation. Including planting cost implies that price stochasticity may shorten the rotation period. Under the mean reverting price process, optimal harvesting becomes more sensitive to periodic price level, as compared to the random walk case. Including risk aversion completely changes the harvesting policy in the sense that, if the forest initially consists of just one age class, it is optimal to smooth the age class structure and have more frequent cuttings from younger age classes. With risk aversion, optimal cuttings depend on price level, even under a random walk price and zero replanting and harvesting costs. In addition, harvesting decisions become dependent on subjective time preference and forest owners' wealth.     

FOREST ROTATIONS AND STAND INTERDEPENDENCY: OWNERSHIP STRUCTURE AND TIMING OF DECISIONS

ABSTRACT. This paper extends the Hartman model to study the optimal rotation age of two interdependent stands at the steady state, when the rotation ages of the two stands are equal and the stream of amenities produced from the two stands may be complements or substitutes, both in space and over time. In the presence of stand interdependence both the ownership structure and the sequence of decision making matters. Rotation age choices are examined and compared under a variety of equilibria, including Nash, Stackelberg and sole owner cases. We show that the sole owner's rotation age is longer than the rotation age under both Nash and Stackelberg assumptions if the stands are spatial complements but shorter if they are spatial substitutes. The precise relationship between the Nash and Stackelberg rotation ages and the qualitative properties of rotation ages in terms of timber prices, regeneration costs and interest rates also depend on how spatial substitutability and complementarity between stands evolves through time.